Any chance of OTA?

Assuming you are in the vicinity of Salem Illinois, do you have any neighbors or houses around town with antennas on their roofs pointed toward St. Louis? This might give you an idea if there have been others who could success fully do what you are proposing.
OTA reception there is not impossible but may be expensive and/or difficult.
Back in the 70's we lived in a town where the transmitter for NBC on channel 8 was some 80 miles away. Everyone had 30-40 ft telescoping masts with guy wires and everything all over town (our antenna was a Finco seen in my avatar), so with a 40 ft tall mast on top of a 20 ft roof with a high power pre-amplified UHF antenna you should b able to get reception but the signal is refracted over two edges.
Look at HDTV Primer for more in depth discussion of fringe TV reception.
Below is my Channel Master CM4228 antenna on a 2 section telescoping mast anchored to the ground and attached to the eave of my house. I don't need a particularly tall mast as I am about 25 miles from the transmitters.
A 40 ft telescoping mast is about $250. If you put up an entire system yourself you are probably looking at an expenditure of around $500.
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I don't like the way network tv looks.